Rangers fans have been accused of "tarnishing" their club's reputation by singing sectarian songs during a pre-season friendly.
Police said the "disappointing" behaviour by some supporters had taken place during Tuesday night's match against Stirling Albion.
A section of fans were warned twice over the tannoy by home team Stirling Albion about the singing.
No arrests were made at the game, which Rangers won 1-0.
A force spokeswoman said: "There was sectarian singing from a section of the visiting support, leading to warnings from the club [Stirling Albion] during the first half.
"Towards the end of the half there was discussion between police and the club about pausing the match to allow further warnings to be delivered.
"It was decided to wait a short time and deliver such warnings at half time. This again was done by the club. At no time did the police recommend that the match be called off."
Once Stirling Albion had issued the warning, and the police presence at the match was increased in the second half, there was a "reduction" in the behaviour, police said.
The incident will now be reviewed by senior police officers.
The spokeswoman added: "It is disappointing that so-called fans have seen fit to disrupt this event and to tarnish the name of their club in this way."
A crowd of more than 1,200 turned out for the match, which was a testimonial for former Stirling Albion owner and chairman of 17 years, Peter McKenzie.
A Rangers spokesman said they had asked Central Scotland Police for CCTV footage so the club could investigate the allegations.
He added: "We are looking into this as we have received a variety of reports about fan behaviour last night, ranging from praise for the fans who attended the game to allegations of sectarian singing by one small group.
"We note there were no arrests and police have confirmed there was no suggestion the game would be stopped at any time."